Epistemology of Disagreement: the Good News 1. David Christensen

Transcription

1 Epistemology of Disagreement: the Good News 1 David Christensen We all live out our lives in states of epistemic imperfection. Most obviously, this is true because the evidence on which we base our beliefs is limited. Only a little less obviously, we live in states of epistemic imperfection because we do not always respond to the evidence we have in the best way. Given that our epistemic condition consists in imperfect responses to incomplete evidence, part of being rational involves taking account of these sources of imperfection. Fortunately, each of us is confronted every day by opportunities for epistemic selfimprovement. Most frequently, opportunity arrives in the form of evidence that bears directly on the subject-matters of our beliefs: hearing the evening weather report, I can revise upward my confidence that it will rain tomorrow. Other opportunities for epistemic self-improvement address not our deficits in evidence, but our deficits in responding to the evidence: reading a study showing that professors vastly overrate their teaching abilities, I can revise downward (at least temporarily) 2 my confidence that I m a dynamite teacher. One fairly common situation that may present opportunities for improvement is that of discovering that another person s belief on a given topic differs markedly from one s own. And it is this sort of opportunity that I want to concentrate on here. How should I react when I 1 This paper was read in the Fall 2004 at Princeton University, and I d like to thank the audience at that talk for stimulating discussion. I d also like to thank the following people for helpful discussions of this material or comments on earlier drafts: David Barnett, Sin yee Chan, Adam Elga, Rich Feldman, Tom Kelly, Hilary Kornblith, Arthur Kuflik, Don Loeb, Bill Mann, Mark Moyer, Derk Pereboom, Jim Pryor, Jonathan Vogel, Adam Wager, and three anonymous referees for the Philosophical Review. 2 See (Elga 2005).

2 2 discover that my friend and I have very different beliefs on some topic? Thinking about belief in a quantitative or graded way, the question concerns cases in which my friend and I have very different degrees of confidence in some proposition P. Should my discovery of her differing degree of belief in P lead me to revise my own confidence in P? 3 In some cases, the answer is easy. Suppose, for example, that friend gives moderate credence to the proposition that I had cereal for breakfast, while I, with my vivid memory of enjoying bacon and eggs, am virtually certain that it s false. Here, the disparity between our beliefs is most reasonably explained by her lacking evidence that I have. Similarly, suppose my friend thinks it highly likely that her child is the best violinist in his school, and can t understand why he hasn t been made first chair. I, who have also heard the child play numerous times, put quite a lower probability on his being best in his school. Again, the obvious explanation for the discrepancy in our beliefs is that it s my friend s problem; this time, it happens to be a problem in how she has responded doxastically to the ample evidence we both have. In both cases, there seems to be little or no reason for me to revise my belief after learning of hers. Other cases resolve themselves, equally obviously, in the opposite direction. If I have reason to believe that my friend has more evidence, or is likely to be better at responding to the evidence, I should change my belief upon learning of hers. 3 Much of the discussion of this issue in the literature is in terms of an all-or-nothing model of belief, rather than the graded model I ll concentrate on. I want to focus first on degrees of belief because I want to look carefully at the rational effects of evidence, and evidence may change degrees of belief even when it doesn t change all-or-nothing beliefs. I will, however, examine the issue in terms of all-or-nothing beliefs below.

3 3 But some cases are more interesting. In particular, there are cases where one does not have any special reason to think that the person with whom one disagrees has more (or less) evidence, or is more (or less) likely to react to that evidence in the right way. Suppose I find out that my friend disagrees with me about P: she has moderately high confidence that it s true, and I have moderately high confidence that it s false. But to the best of my knowledge, my friend is just as well-informed as I am--in fact, we may suppose that my friend and I have had long discussions in which we share every bit of evidence we can think of that s relevant to P. And suppose further that I have good reason to believe that my friend and I are equally intelligent and rational, and that I know of no general reason (like the fact the people tend to be biased towards their children) to think either of us is especially likely to be particularly good, or bad, at reacting to evidence on this particular topic--no reason, that is, aside from the fact that my friend disagrees with me about P. In other words, my friend seems to be what some have called an epistemic peer. In this sort of case, should I revise my belief? Some have worried that if I cannot hold onto my beliefs in the face of disagreement by apparent epistemic peers, I ll be forced into an unacceptable degree of skepticism about controversial areas, such as philosophy, politics and morality. Peter van Inwagen puts the problem, as it applies to philosophical beliefs, as follows (here by philosophical skeptics van Inwagen means people who can t see their way clear to being nominalists or realists, dualists or monists,... people who have listened to many philosophical debates but have never declared a winner ): I think that any philosopher who does not wish to be a philosophical skeptic--i know of no philosopher who is a philosophical skeptic--must agree with me that... it must be possible

4 4 for one to be justified in accepting a philosophical thesis when there are philosophers who, by all objective and external criteria, are at least equally well qualified to pronounce on that thesis and who reject it. (1996, 275) Van Inwagen extends his point to politics and to his ultimate target, religious belief. Others have expressed similar worries. 4 I will argue that in a great many cases of the sort van Inwagen and others seem to have in mind, I should change my degree of confidence significantly toward that of my friend (and, similarly, she should change hers toward mine). I will first examine an initially attractive way of denying that the disagreement of peers should typically occasion belief-revision. I ll then consider some simple, somewhat idealized cases that motivate a general demand for revision; develop and defend an account of when and why belief-revisions are called for; examine the effect of relaxing the idealizations involved in the central cases; and finally explore the extent to which the position I defend entails an objectionable degree of skepticism. 1. Why not Live and Let Live? One reason for doubting that the disagreement of peers should typically occasion beliefrevision flows from a permissive conception of rational belief. 5 It seems plausible, at least at first, that there could be more than one completely reasonable epistemic response to a given evidential 4 See (Plantinga 2000, ch. 13) for a somewhat similar argument concentrating on moral examples. Kelly (2005) and Feldman (ms.) also see a threat of skepticism as flowing from the claim that disagreement by peers should occasion changing one s beliefs. 5 This sort of conception is defended in (Rosen 2001).

5 5 situation. Perhaps, two people could share all relevant evidence, react to that evidence faultlessly, and yet reach different conclusions. If that is possible, then it might seem that in the case of disagreement with a peer, one could adopt what Adam Elga once called (in correspondence) a live-and-let-live attitude. The live-and-let-live attitude seems, at least at first, appealingly openminded. One might think, She has her belief, and I have mine. Our evidence is the same, but for all I know we re both perfectly rational in our reactions to this evidence. To refuse to adopt this attitude might seem to betray an insufficient appreciation of epistemic diversity. 6 But it seems to me that the live-and-let-live attitude is hard to maintain--or, at least, that it should be. To see why, let us focus in on a specific case. Suppose that my friend and I are doctors in the same practice. One of my patients is in very serious condition, and my friend and I both examine him, study his medical records, read the relevant literature--and come to conflicting conclusions. There are, it turns out, just two theories that might explain his symptoms. Theory A is somewhat simpler, but Theory B fits a bit better with the data. My friend has about 65% credence in theory B and 35% in A, while for me, the two figures are reversed. When my friend and I talk the case over as thoroughly as two intelligent people can ever discuss anything, we come to see that she is more moved by the fit with reported data, while I m more moved by simplicity. I take it that this is at least one sort of case--somewhat different weightings of fully reasonable epistemic desiderata--that make plausible the idea that rationality is not so restrictive as to single 6 Richard Feldman (forthcoming), (ms.) considers, and rejects, this way of defusing disagreements, for reasons similar to those offered below. My term Rational Uniqueness, referring to the assumption that there is a unique maximally rational response to a given evidential situation, is intended to echo Feldman s Uniqueness Thesis, which is essentially the same idea applied to all-or-nothing (as opposed to graded) beliefs.

6 6 out one rational response to each evidential situation. How should I react to my friend s belief in this case? It seems to me that there s considerable pressure for me to do at least one of two things: (1) to think that my friend has not given the right relative weights to simplicity and fit with data, and hence that she has not responded to the evidence maximally rationally; or (2) to move my belief in the direction of hers. There s something unstable about holding onto my belief while acknowledging that a different belief enjoys equal support from the evidence. 7 This seems particularly clear if important things hang on the belief in question. Suppose that theories A and B would mandate different and mutually incompatible medical treatments. If A is true, one treatment is vastly more likely to save the patient s life, while if B is true the other treatment is much more likely to succeed. We might even suppose that I discover the treatment mandated by theory A (the one I favor) to involve excruciating pain. Given that the patient s life is at stake, if the A-mandated treatment has a significantly greater chance of saving him (as it does if we take theory A to be 65% likely to be true), there s no question that it s what I should prescribe. But it seems wrong for me to say to my friend, Well, I admit that you have considered all the same evidence as I have, and I admit that your putting the probability of theory A at only 35% enjoys just as much rational support from our evidence as does my putting the probability at 65%. But I ve come to come to the latter opinion, so I m recommending the excruciatingly painful procedure. 7 A point along similar lines is made by Roger White (2005). See White s paper for a more thorough criticism of permissive notions of epistemic rationality.

7 7 Here s another way to think about the question: do I think that her weighting leads in general to equally accurate beliefs? If so, then why think my belief is likely to be more accurate now? I could, of course, be lucky. But it would seem clearly wrong for me to put my patient through excruciating pain on the assumption that I lucked out. On the other hand, if I think her weighting does not lead in general to equally accurate beliefs, why should I grant that it s just as rational to form beliefs using that weighting? 8 And so it seems to me doubtful that one can invoke a permissive notion of rationality to dismiss the significance of the opinions of otherwise rational people with whom one disagrees. Interestingly, the live-and-let-live attitude, despite its initial open-minded flavor, ends up allowing an implausibly closed-minded attitude toward the beliefs of others. So let us proceed for the present on the assumption that there is only one maximally rational response to a given evidential situation. I will, however, explore the effects of relaxing this assumption below. 9, 10 8 I should note that to say that I believe my weighting policy is more rational than hers need not commit me to being able to give an ultimately non-question-begging defense of my policy. Hume, I think, showed us that this cannot be the standard for rational belief-forming policies. But to the extent that I regard it as my duty to prescribe the painful treatment, I must regard my colleague in somewhat the way I regard the counterinductivist: she s not completely rational, even if I can t demonstrate that. We should not take the impossibility of non-questionbeggingly demonstrating that one method of forming beliefs is uniquely rational to show that more than one method of forming beliefs is rationally acceptable. (Compare (Feldman forthcoming, III B), which may reject my view here.) 9 It might seem that once one thinks in degree-of-belief terms, the alternative to a permissive notion of rational belief is obviously untenable. Many have noted that in situations in which the evidence bearing on some proposition P is relatively meager, it does not seem that one unique number could possibly be singled out as the uniquely rational degree of belief in P. But rejecting permissive conceptions of rationality need not commit one to representing the rational response to every evidential situation with a single probability function. Most favor using sets of such functions (see (Kaplan 1996, 23 ff) for a version of this view and references to others). (continued...)

8 8 2. Some Simple Cases Let us begin by considering some cases of disagreement in which it s as clear as possible that my friend and I have the same evidence, and that we re in general equally good at responding to that sort of evidence. I take these to be cases where my friend, to use van Inwagen s terms, by all objective and external criteria [is] at least equally well-qualified to pronounce on the relevant issue: Suppose that five of us go out to dinner. It s time to pay the check, so the question we re interested in is how much we each owe. We can all see the bill total clearly, we all agree to give a 20% tip, and we further agree to split the whole cost evenly, not worrying over who asked for imported water, or skipped desert, or drank more of the wine. I do the math in my head and become highly confident that our shares are $43 each. Meanwhile, my friend does the math in her 9 (...continued) On this sort of view, one can hold that the uniquely rational response to an evidential situation is representable by a particular set of probability assignments, and the uniquely rational attitude toward proposition P is represented by a particular range of values between 0 and Another reason that might be given for adopting a permissive conception of rationality is that rationality is likely to be a vague concept. So there won t be one response that the evidence precisely mandates. But vagueness does not entail permissiveness. Suppose that it s vague whether a 0.57 degree of belief in P is rational (or, thinking in terms of the type of model described in the previous note, suppose it s vague whether 0.57 is assigned to P by a member of the rational set of probability functions). Obviously, that does not entail that one is rationally permitted to have a 0.57 degree of belief in P (or have a belief state described by a set of probability functions one of which assigns 0.57 to P). And if it s vague whether your belief or my belief is rationally preferable, that does not show that our beliefs are rationally on a par. Thus there s no straight road from the vagueness of the boundaries of rational belief to a permissive account of rationality. For a somewhat related discussion of vagueness, see (Feldman ms.). Feldman argues that vagueness in the relation between evidence and all-or-nothing belief would not allow full disagreement cases (where I believe P and my friend believes not-p).

9 9 head and becomes highly confident that our shares are $45 each. How should I react, upon learning of her belief? I think that if we set the case up right, the answer is obvious. Let us suppose that my friend and I have a long history of eating out together and dividing the check in our heads, and that we ve been equally successful in our arithmetic efforts: the vast majority of times, we agree; but when we disagree, she s right as often as I am. So for the sort of epistemic endeavor under consideration, we are clearly peers. Suppose further that there is no special reason to think one of us particularly dull or sharp this evening--neither is especially tired or energetic, and neither has had significantly more wine or coffee. And suppose that I didn t feel more or less confident than usual in this particular calculation, and my friend reports that she didn t either. If we set up the case in this way, it seems quite clear that I should lower my confidence that my share is $43, and raise my confidence that it s $45. In fact, I think (though this is perhaps less obvious) that I should now accord these two hypotheses roughly equal credence. The restaurant case is designed to be simple in two ways: in the evidential situation, and in the evaluation of the general capacities my friend and I exercise in reacting to that sort of evidential situation. This makes our intuitions about the case particularly clear. But the same lessons emerge, I think, from cases involving a bit more complexity. Let us consider a case that more closely resembles more interesting cases of disagreement. Suppose I m a meteorologist who has access to current weather data provided by National Oceanic and Atmospheric Administration, the National Weather Service, etc., and that I have learned to apply various models to use this data in making predictions. To make this less like the restaurant case and more like many cases of real-life disagreement, let us suppose that applying the

10 10 models is not just a matter of clear-cut calculation--say, it involves similarity judgments. After thoroughly studying the data and applying the various models I know, I come to have a 55% level of credence in rain tomorrow. But then I learn that my classmate from meteorology school--who has thoroughly studied the same data, knows the same models, etc.--has arrived at only a 45% level of credence. We may even suppose that we have accumulated extensive track records of past predictions, and she and I have done equally well. (We might have been scored by Brier score 11 on our probabilistic forecasts, or asked to answer yes/no questions, and scored for percentage correct.) Should I take her opinion into account and reduce my confidence in rain? It seems obvious to me that, absent some special reason for thinking that I had some advantage over her in making this forecast, I should revise my belief. 12 Even when the evidence does not entail the answer to the relevant question, disagreement of an epistemic peer provides reason for belief-revision. From my point of view, this is a good thing: other people s opinions, in these circumstances, present opportunities for epistemic improvement. But others would reject this verdict. In the next few sections, then, I ll examine some of their objections, with an eye toward developing and defending an account of how and when the disagreement of epistemic peers should occasion belief-revision. 3. Explaining Disagreements and Adjusting Beliefs 11 The Brier score is a standard way of measuring accuracy of probabilistic forecasts. It averages the squared differences between the forecaster s announced probabilities for propositions and the propositions truth values (where 1 is true and O is false). 12 Feldman (forthcoming), (ms.) draws similar morals (in terms of all-or-nothing belief) from similar cases.

11 11 The intuition supporting belief-revision in the meteorology case depends on my acknowledging that my friend is as likely as I am to react correctly to the data we have. But it might be objected that even if I have ample reason to think my friend is in general as good as I am at predicting the weather, in this particular case, I have some special evidence that she s made a mistake. After all, I believe that the data support a 55% credence in rain, and her credence in rain is only 45%. My general reason for trusting my friend is defeated in this case by her reaching what to my mind is the wrong conclusion. Richard Foley (2001) expresses thoughts along roughly these lines, at least in cases where one does not have much information about the person with whom one disagrees. Foley s general position is that my indispensable trust in my own cognitive faculties, combined with the similarity between my faculties and the faculties of others, grounds a presumption in favor of believing as others do. But this presumption is defeasible by information that the other person has a history of errors, lacks important evidence, is poorly trained or is cognitively impaired. And, in addition, Foley writes:... there is an important and common way in which the prima facie credibility of someone else s opinion can be defeated even when I have no specific knowledge of the individual s track record, capacities, training, evidence or background. It is defeated when our opinions conflict, because, by my lights, the person has become unreliable. (2001, 108) Foley says that I might still have reason to defer to the other person s opinion, but only if I have special reasons indicating that he or she is better positioned than I to assess the claim in

12 12 question. 13 Applied to the case of degrees of belief rather than beliefs taken in an all-or-nothing way, he writes the following about the case where the other person s degree of belief in P conflicts with mine:... the prima facie reason I have to trust your opinion is defeated, and hence I have no reason to move my opinion in the direction of your opinion unless I have special reasons for thinking that you are in an especially good position to assess P. 14 Thomas Kelly (2005) develops in greater detail a somewhat similar argument for the legitimacy of sticking with one s original belief in cases of conflict. He specifically addresses cases like the weather-forecasting case, where I reasonably believe that there is an initial symmetry in both evidence and ability to react to evidence between my friend and me: Suppose that, as it turns out, you and I disagree. From my perspective, of course, this means that you have misjudged the probative force of the evidence. The question then is 13 See (Foley 2001, 110). Foley s position (at least with respect to all-or-nothing belief) is more nuanced than this passage may suggest. He says that one shouldn t defer (that is, adopt the other person s belief) unless one has reason to think the other person better positioned. But if one has special reason to think the other person is equally well-positioned (as would be the case in an all-or-nothing belief version of our weather-forecasting case), he thinks one should suspend belief. Lacking special information about the other person, however, one should not even suspend. I will discuss cases in which one lacks such special information below. For the present, I want just to focus on the basic idea that disagreement by itself serves to undermine the evidential import of another s beliefs. 14 (Foley 2001, 114). Note that Foley here seems to reject any change in degree of belief unless I have reason to believe that my friend is actually better-positioned. This seems to go against the spirit of advocating suspension of all-or-nothing belief when I have special reason to think my friend equally well-placed. Since Foley concentrates mainly on all-or-nothing belief, this last quoted passage may not represent his considered view.

13 13 this: why shouldn t I take this difference between us as a relevant difference, one which blocks the otherwise perfect symmetry? It seems to me that there is clearly something right about this line. As applied to the weather case, my discovering that my friend has reached what seems to me the wrong conclusion does constitute evidence that she has made a mistake, and thus does give me reason to trust her opinion less than I ordinarily would. However, another point needs equal emphasis: the fact that she disagrees with my prediction also constitutes evidence that I have made a mistake. 15 So it s not clear so far that any asymmetry has developed. To focus in on the symmetry question, let me begin with an admittedly crude analogy: I look at my watch, a one-year-old Acme that has worked fine so far, and see that it says 4:10. Simultaneously, however, my friend consults her watch--also a one-year-old Acme with a fine track record--and it reads 4:20. When she tells me this, it clearly gives me new evidence that her watch is fast: I should not trust her watch as much as I would have before finding out that it disagreed with mine. But just as clearly, I ve just gotten new evidence that my watch is slow, and this should diminish my trust in it. In this case, it s obvious that the fact that one of the watches is on my wrist does not introduce an epistemically relevant asymmetry. But perhaps the watch example misleads by introducing a third-person perspective into the picture: my watch s mechanism is not part of me. Kelly cites Foley s claim that [I]t is deeply misleading to think about [conflicts of opinion] in terms of a model of neutral arbitration between conflicting parties (Foley 2001, 79). And it is certainly true that when I consider how to regard 15 This point is also noted in (Trakakis ms.).

14 14 my friend s disagreement, I must do so from within the first-person perspective--that is., using my own beliefs. Might this give my beliefs--which include my belief about the matter on which my friend and I disagree--a kind of privileged position that the watch on my wrist doesn t share? Let us consider, then, whether taking a first-person perspective on this sort of situation provides an asymmetry that is epistemically relevant in assessing evidence of error. It seems to me that there is considerable support for symmetry even from within a firstperson point of view. Consider how the weather-forecasting example might unfold over time. Before we come up with our forecasts, my friend and I know that our skills, education and track records are equally good, and that we ll be spending the same time studying the same data. Suppose we consider in advance the question of who will be more likely to have made a mistake if we end up disagreeing. We might even wonder who will be more likely to have made a mistake if she ends up putting the probability of rain at 45% and I put it at 55%. I take it as obvious that each of us--from within his or her own, first-person, perspective--should say, in advance, that we re equally likely to make an error in such a case. And now suppose we do our analyses, we each feel confident in our reasoning, we announce the results, and find out that we have, indeed, come up with different predictions: she has actually come up with 45% and I with 55%. At this point, has an asymmetry developed that would be relevant to the question of who was more likely to have made a mistake? True, I may now have in mind, or directly feel the force of, the reasoning supporting my answer, and not the reasoning supporting hers. But can this development suddenly license me in thinking that her reasoning is more likely to be mistaken than mine? It seems to me that it cannot. After all, when I said, before we did our analyses, that we d be equally likely to have made a mistake in the case of conflict, I knew that in such a case I d have

15 15 in mind some apparently convincing reasoning behind my answer. Now I do have such reasoning in mind, as does my friend, of course. But I cannot see how this would provide me with any justification to think now that my reasoning is less likely to be mistaken. 16 Thus it seems to me that taking a first-person perspective on the situation does not licence me in thinking that disagreement with my friend is better explained by her error than by mine. Given that my friend and I are generally reliable thinkers who have studied the same evidence, the fact that we disagree will be explained by the fact that at least one of us has made a mistake in this case. But intuitively, the explanation in terms of my friend s mistake is no more reasonable than the explanation in terms of my mistake. And I should acknowledge this by moving my belief toward hers. Of course, putting the issue in terms of assessing explanations for the disagreement does not, all by itself, provide an illuminating account of the force of disagreement. For it raises the question: what are the conditions under which explanations involving my friend s error (rather than my own error) are more reasonable? The fact that I must assess these explanations from within my own perspective means that I ll inevitably assess them by using my own beliefs. But it seems clear that some ways of using my beliefs in arriving at an assessment are not reasonable. I cannot now say, We have to explain why my friend and I disagree about the probability of rain. The 16 Of course, it could be that during the time of coming up with the prediction, I get some new evidence bearing on the question of who s more likely to make a mistake: I may feel unusually sleepy and distracted, or especially crisp and alert; or I may see my friend yawning, or concentrating intensely. But this would just be like the case of conflict with someone antecedently known not to be an epistemic peer. The question at issue here is whether I, having come up with 55%, should take the mere fact that my friend now puts the probability of rain at 45% as evidence that she is more likely than I to have made an error.

16 16 data indicate that it s 55%. Since my friend has arrived at 45%, it must be she who made the error. So the important question is this: how am I to use my beliefs in assessing the reasonableness of the two explanations in a way that does not just beg the question in favor of the opinion I currently hold? In seeing how I might be able to do this, let us look back to some more straightforward cases in which it seems clear that disagreement may be discounted substantially without begging the question. Some beliefs--such as high confidence that one is the messiah--are recognized signs of general mental derangement. Other beliefs--such as those involving the sterling qualities of one s children--tend to be held irrationally, even by otherwise rational people. So if my friend disagrees with me by being quite confident that she is the messiah, or that her child is the best violinist in the school, I clearly have some reason to think that the best explanation of our disagreement is that she has made an error. In these cases, it is salient that my reason for favoring the explanation in terms of her error is in an important way independent of my reasoning about the issue on which my friend and I disagree. My beliefs about the relevant general psychological mechanisms do not depend on the question of whether my friend in particular is the messiah, or has stunningly exceptional children. This presents a clear contrast with the restaurant or weatherprediction cases, where I seem to lack grounds (independent of my own reasoning on the disputed matter) for favoring the explanation in terms of my friend s error. These cases, then, suggest the following (admittedly rough) principles for assessing, and reacting to, explanations for my disagreement with an apparent epistemic peer: (1) I should assess explanations for the disagreement in a way that s independent of my reasoning on the matter under dispute; and (2) to the extent that this sort of assessment provides reason for me to think that the

17 17 explanation in terms of my own error is as good as that in terms of my friend s error, I should move my belief toward my friend s. 17 In the next section, I ll examine this account a bit more closely, with an eye toward both making the principles more precise and defending them against plausible objections. 4. Some Tests and Clarifications We might begin by considering an apparent counterexample to this account. Consider an (admittedly unrealistic) variant on the restaurant case, in which my friend becomes confident that our shares of the check are $450--quite a bit over the whole tab. Here, I think that I need not significantly reduce my confidence in my $43 answer, or raise my very low confidence in the $450 answer. 18 Let us concentrate on our disagreement about whether our shares are $450. I think it is initially far from clear that my reasons for selectively suspecting my friend to be in error are truly independent of the reasons on which I base my own belief. If asked why I think my friend is wrong, I d naturally say something like Well, $450 just can t be right--it s higher than the whole bill! But this is exactly the reason I m so confident that $450 is false. So the puzzle is: why does it seem right to discount my friend s belief in this Extreme Restaurant Case, but not in the Regular Restaurant Case we looked at earlier? (Elga ms.). 17 A more formal proposal, very much in the same spirit as (1) and (2), is put forward in 18 Should I change my belief at all? My hedge significantly is intended only to acknowledge the (extremely remote) possibility that, for instance, one of my dining companions quietly ordered a bottle of obscenely expensive wine, and I also badly misread the total on the bill. Insofar as my friend s answer of $450 would confirm such an (extremely improbable) possibility, some (extremely tiny) adjustment in my beliefs could be in order.

18 18 One answer that suggests itself immediately is that it s simply my initial high level of certainty that my share is not $450 which justifies me in discounting my friend s confidence that it is $450. But this seems suspect right away, since in the Regular Restaurant Case, I might well have quite a high initial degree of confidence in my answer--maybe I ve been right 99% of the time. Yet this seems to give me virtually no reason to favor the explanation in terms of my friend s mistake, given that she has a similar record. And we can also devise cases where I should move my belief considerably toward my friend s, even though I start with a perfectly rational % confidence that P is false. Consider a million-ticket lottery in which each ticket is printed with three 6-digit numbers which, when added, yield the 7-digit number that is entered into the lottery. My friend has a ticket, and of course I am extremely confident that her ticket did not win. But just to pass the time, I add the numbers in my head and check the result against the winning number printed in the paper. No match, so I remain extremely confident that she hasn t won. But then she adds the figures in her head, checks the result against the paper, and announces that she s won! Here, it seems clear--insofar as I can rationally discount the probability that my friend is just joking, so that this really is a case of disagreement--that I should move my level of confidence in her ticket losing way down below the million-to-one level. So it seems that what determines the correct reaction to finding out about my friend s disagreement is not simply my level of confidence in the proposition about which we disagree. What, then, differentiates the Lottery Ticket Case from the Extreme Restaurant case? It seems to me that a key to the difference can be seen by focusing not on the proposition under dispute, but on the reasoning processes on which my opinion, and my friend s opinion, are based.

19 19 Let s first consider the Lottery Ticket Case. Here, my confidence that her ticket didn t win was based both on reasoning from general facts about the lottery and on my mental addition. My friend s very different level of credence is based on that same general reasoning about the lottery and on her mental addition. The explanation for our disagreement clearly lies in the fact that at least one of us made an adding mistake. But even though it was initially rational for me to be extremely confident that her ticket lost, it is not rational for me, after learning of her disagreement, to think that she is more likely to have made an adding mistake than I am. And if her having made an adding mistake is no more likely than my having made one, I cannot maintain my extremely high initial level of confidence that her ticket lost. Contrast this with the Extreme Restaurant Case, and let us again concentrate on the claim that our shares of the bill are $450. Here, as we ve seen, the reasoning behind my being so confident in the falsity of this claim goes well beyond the calculations by which I arrived at $43. My belief is also supported by my reasoning that my share cannot be greater than the whole bill. This is the sort of common-sense check that math students in middle school are taught to use to catch arithmetic errors. On the other hand, as the case was set up, I have no reason to suppose that my friend has checked her answer in this way. In fact, I have good reason to doubt that she has. It is much more likely that she calculated and has not brought common-sense checking to bear. Now I take it that this sort of common-sense checking is much less liable to error than mental arithmetic. In fact, if I had come up with $450 in my own calculation and then had done the common-sense check, I, like the diligent middle-schooler, would immediately have rejected the

20 20 calculation. 19 Thus, given what it s reasonable to believe about the reasoning supporting my friend s and my differing beliefs, it seems that the best explanation of our disagreement here lies in my friend s error. This is why I should not significantly revise my belief. If this is right, the Extreme Restaurant case does not undermine the principle that in evaluating competing explanations of disagreement about P, my evaluation should be independent of the reasoning which supports my current assessment of P. Although it might be natural for me to say in the Extreme Restaurant Case Well, my share can t be that high, so she s wrong, that would not really describe why I should favor the explanation in terms of her error. After all, saying that would be parallel to saying It s $43, so she s wrong in the Regular Restaurant Case. The real ground for thinking that my friend made the error in the Extreme Restaurant Case derives from the fact I have evidence that my assessment of the disputed proposition is supported by an extremely reliable kind of reasoning, but I have no basis for supposing the same about my friend s contrary assessment. 20 My grounds for discounting my friend s belief are based on considerations about my reasoning, but not on that reasoning itself. There may still be some feeling that my reason for favoring the friend s-error explanation in the Extreme Restaurant Case must somehow flow from the brute convincingness of the common- 19 Thanks to Adam Wager for pointing out how this observation supports the claim that my trust of my common-sense reasons over my friend s calculation is quite independent of who performed the calculation. 20 We might even consider a third restaurant case, where my friend is a child just learning to do arithmetic. If she gets $45, I will quite reasonably think she s the one who s wrong, and not adjust my confidence significantly. I might also gloss my reason for thinking her wrong by saying It s $43, so she s wrong. But my reason for treating our beliefs asymmetrically--for thinking that she s more likely to be wrong than I--derives from my general beliefs about our calculating abilities, not from my particular calculation.

21 21 sense considerations; that my talk of an extremely trustworthy kind of reasoning is merely cover for my using the reason for my assessment of P over again, as a reason for favoring the friend serror explanation of our disagreement. It is hard to think of a case in which I have this kind of powerful reason for my assessment without having overall reason to favor the friend s-error explanation. In the Extreme Restaurant Case, there seems to be no natural candidate for an equally trustworthy sort of reasoning that my friend could be employing, and it s hard to see how to add one to the case in an intuitively plausible way. Still, I think we might without too much intuitive absurdity devise a case in which I have the sort of compelling reason I have in the Extreme Restaurant Case, and yet where I don t have reason to favor the explanation in terms of my friend s error. Suppose that I have the sort of calculational abilities associated with savant syndrome. People with this sort of ability (though usually severely mentally impaired in other ways) have phenomenal abilities to perform calculations very quickly, with amazing accuracy and confidence, in their heads--calculations that ordinary people would find difficult to perform much more slowly with pencil and paper. Some of the people who have this sort of ability are not consciously aware of using any algorithm to solve the problems; they seem to just see that the answer is correct. 21 Suppose that my friend and I both have the ability to determine in this way whether 8-digit numbers are prime. We re both equally extremely accurate, though neither of us is infallible--each of us, very rarely, sees things wrong. We re presented with an 8-digit number, and it seems to me that I can just see that it s prime. However, my friend disagrees, and after discussing the matter with her, I become 21 Oliver Sacks (1985, ch. 23) describes this sort of case.

22 22 convinced that it seems to her that she can just see that the number isn t prime. Here, to the extent that I can discount the probability that she s joking, and to the extent that I have evidence that she s not drunk, or especially tired, etc., it seems that I should move my belief. After all, I know that I m fallible on this sort of question, and that my friend s record is as good as mine. And this is true even though it still seems to me that I can see that my answer is correct. This suggests that even in cases such as the Extreme Restaurant Case, where one is reasonable in laying the error at one s friend s feet, one s doing this is not rendered reasonable simply by the force of one s own assessment of the disputed claim. This not to say, however, that my degree of confidence in my initial opinion is always (or even typically) irrelevant to how I should react to disagreement; in fact, quite the opposite is true. Typically, when I am highly confident in my initial opinion, I have good reason to think that the opinion is based on highly reliable reasoning. But this itself gives me some reason to think that an equally-informed person who disagrees with me did not use the same sort of reasoning I did, since it is unlikely that two people using a highly reliable method of reasoning on the same evidence would reach different opinions. So in many cases where I know relatively little about the person with whom I disagree, my having a great deal of confidence in my initial opinion should correlate with my giving less credence to the opinion of the other person. But my discounting the opinions of others when I m highly confident in my initial opinion and know little about the others reasoning processes does not in the end constitute being partial to my own views just because I confidently hold them. For to the extent that I have evidence that my equally-informed friend did in fact use the same sort of reasoning on which my initial opinion was based, I lack reason for favoring my own opinion. These cases, then, do not undermine the impartial principle that I

23 23 should assess explanations of disagreement in a way that s independent of the reasoning on which my current assessment of the disputed proposition is based. Let us look briefly at the second principle advanced above--that, to the extent that my assessment provides reason for me to think that the explanation in terms of my own error is as good as that in terms of my friend s error, I should move my belief toward hers. One of the ways in which this principle is underdeveloped is that I haven t specified any mechanism for determining the degree to which I should move my belief in various cases. I cannot attempt that here in any detail. But, to be a bit more specific, I think that the right way to develop a more precise version of the principle would have the following result: when I have excellent reason to think that the explanation in terms of my own error is every bit as good as that in terms of my friend s error, I should come close to splitting the difference between my friend s initial belief and my own. To see why this is reasonable, consider a variant on the doctor case discussed above. Once again, let my initial credences in diagnoses A and B be 65% and 35% respectively, and my friend s credences the reverse, and let us both feel equally clear-headed, confident in our reasoning, etc. This time, however, suppose I know from extensive experience that my friend s reasoning tends to be just a little more reliable than my own. On which diagnosis should I base my emergency treatment? I think I should go with B, even though I directly feel the pull of only my own reasoning (if this isn t sufficiently clear, think about what you would want me to do if you were my patient). And the reason I should base my treatment on B is surely because it s now rational for me to have a bit more confidence in B than in A. In other words, if my friend s reliability is just a little bit better than mine, I should more than split the difference with her. But if I should

24 24 move closer to her initial belief than to mine when she s just a bit more reliable, there seems little reason to deny that I should split the difference evenly when we re fully peers. 22 Of course, both of the principles discussed above are fairly rough, in various ways. But even without a precise recipe for determining what are the reasons on which I base my belief about P, or for adjudicating goodness of explanations, or for calculating the degree to which I should alter my belief in response to learning of a peer s disagreement, I think it s clear that there are a great many cases in which, intuitively, I may put aside the reasons on which I base my own assessment of P, and see that I have overall reason to think that my friend and I are equally likely to have made the sort of mistake that would explain our disagreement. In such cases, I should revise my belief considerably. There is, I think, no reason to suppose that taking the required sort of semi-detached perspective toward my beliefs should be impossible from the first-person perspective. The firstperson perspective is not the dogmatic perspective: it does not entail denying or ignoring the possibility that I have made a cognitive error. The first-person perspective surely poses no barrier to my accepting correction from my friends whom I believe to be smarter, or less biased, or in other ways better at reacting to the evidence. And once this is granted, there seems to be little reason for supposing that it presents some obstacle to my using my epistemic peers as checks on my own thinking. 23 Fortunately, trapped though I am in my own epistemic perspective, I am 22 The question of how to take into account disagreement of other near-peers, and not-sonear-peers, will be discussed below. 23 See (Christensen 2000, section 5) for related discussion.

25 25 perfectly capable of taking an impartial attitude toward some of my own beliefs, and using the varied opinions of others as resources for my own epistemic improvement. If something along the above lines is right, disagreement matters more than some might seem to think. Van Inwagen, discussing those who hold political beliefs contrary to his own, writes: These people are aware of (at least) all the evidence and arguments that I am aware of, and they are (at least) as good at evaluating evidence and arguments as I. How, then, can I maintain that the evidence and arguments I can adduce in support of my beliefs actually support my beliefs?... Well, as with philosophy, I am inclined to think that I must enjoy some sort of incommunicable insight that the others, for all their merits, lack. (1996, 277) Notice that van Inwagen does not claim to be able to point to any reason, independent of the disagreement itself, for thinking that those who disagree with him lack some special insight he has. But if the above reasoning is correct, having some such independent reason is precisely what one would need, to maintain rational confidence in the face of disagreement with apparent peers. If my evidence that my (otherwise equally-reliable) friend lacks insight on some political issue P is just that she disagrees with my firmly-held belief that P, then I m in no better position than I am in the weather-forecasting case when I discover that my (otherwise equally-reliable) meteorologist friend disagrees with me. The mere fact of disagreement, after all, cannot show that I am the one who must have the epistemic edge. If my political or metaphysical or religious disagreements with others resemble the weather-prediction case more than they do the case of the child s musical talent, then insofar as I fail to take my friends beliefs into account in revising mine, I believe irrationally.